What is a transverse wave, Grade 10 Physics 1/ What is a transverse wave We have studied pulses in Chapter 5, and know that a pulse is a single disturbance that travels through a medium. A wave is a periodic, continuous disturbance that consists of a train of pulses. Definition: Wave A wave is a periodic, continuous disturbance that consists of a train of pulses. Definition: Transverse wave A transverse wave is a wave where the movement of the particles of the medium is p erpendicular to the direction of propagation of the wave. Activity :: Investigation : Transverse Waves Take a rope or slinky spring. Have two people hold the rope or spring stretched out horizontally. Flick the one end of the rope up and down continuously to create a train of pulses. Describe what happens to the rope. Draw a diagram of what the rope looks like while the pulses travel along it. In which direction do the pulses travel? Tie a ribbon to the middle of the rope. This indicates a particle in the rope. Flick the rope continuously. Watch the ribbon carefully as the pulses travel through the rope. What happens to the ribbon? Draw a picture to show the motion of the ribbon. Draw the ribbon as a dot and use arrows. In the Activity, you have created waves. The medium through which these waves propagated was the rope, which is obviously made up of a very large number of particles (atoms). From the activity, you would have noticed that the wave travelled from left to right, but the particles (the ribbon) moved only up and down. Figure 6.1: A transverse wave, showing the direction of motion of the wave perpendicular to the direction in which the particles move. When the particles of a medium move at right angles to the direction of propagation of a wave, the wave is called transverse. For waves, there is no net displacement of the particles (they return to their equilibrium position), but there is a net displacement of the wave. There are thus two different motions: the motion of the particles of the medium and the motion of the wave. 2/ Peaks and Troughs Waves consist of moving peaks (or crests ) and troughs. A peak is the highest point the medium rises to and a trough is the lowest point the medium sinks to. Peaks and troughs on a transverse wave are shown in Figure 6.2. Definition: Peaks and troughs A peak is a point on the wave where the displacement of the medium is at a maximum. A point on the wave is a trough if the displacement of the medium at that point is at a minimum. 3/ Amplitude and Wavelength There are a few properties that we saw with pulses that also apply to waves. These are amplitude and wavelength (we called this pulse length). Definition: Amplitude The amplitude is the maximum displacement of a particle from its equilibrium position. Activity :: Investigation : Amplitude Fill in the table below by measuring the distance between the equilibrium and each peak and troughs in the wave above. Use your ruler to measure the distances. What can you say about your results? Are the distances between the equilibrium position and each peak equal? Are the distances between the equilibrium position and each trough equal? Is the distance between the equilibrium position and peak equal to the distance between equilibrium and trough? As we have seen in the activity on amplitude, the distance between the peak and the equilibrium position is equal to the distance between the trough and the equilibrium position. This distance is known as the amplitude of the wave, and is the characteristic height of wave, above or below the equilibrium position. Normally the symbol A is used to represent the amplitude of a wave. The SI unit of amplitude is the metre (m). Worked Example : Amplitude of Sea Waves Question: If the peak of a wave measures 2m above the still water mark in the harbour, what is the amplitude of the wave? Answer The definition of the amplitude is the height that the water rises to above when it is still. This is exactly what we were told, so the amplitude is 2m. Activity :: Investigation : Wavelength Fill in the table below by measuring the distance between peaks and troughs in the wave above. What can you say about your results? Are the distances between peaks equal? Are the distances between troughs equal? Is the distance between peaks equal to the distance between troughs? As we have seen in the activity on wavelength, the distance between two adjacent peaks is the same no matter which two adjacent peaks you choose. There is a fixed distance between the peaks. Similarly, we have seen that there is a fixed distance between the troughs, no matter which two troughs you look at. More importantly, the distance between two adjacent peaks is the same as the distance between two adjacent troughs. This distance is call the wavelength of the wave. The symbol for the wavelength is λ (the Greek letter lambda) and wavelength is measured in metres (m). Worked Example: Wavelength Question: The total distance between 4 consecutive peaks of a transverse wave is 6 m. What is the wavelength of the wave? Answer Step 1 : Draw a rough sketch of the situation Step 2 : Determine how to approach the problem From the sketch we see that 4 consecutive peaks is equivalent to 3 wavelengths. Step 3 : Solve the problem Therefore, the wavelength of the wave is: 3λ = 6 m => λ = 2 m 4/ Points in Phase Activity :: Investigation : Points in Phase Fill in the table by measuring the distance between the indicated points What do you find? In the activity the distance between the indicated points was the same. These points are then said to be in phase. Two points in phase are separate by an integer (0,1,2,3,...) number of complete wave cycles. They do not have to be peaks or troughs, but they must be separated by a complete number of wavelengths. We then have an alternate definition of the wavelength as the distance between any two adjacent points which are in phase. Definition: Wavelength of wave The wavelength of a wave is the distance between any two adjacent points that are in phase. Points that are not in phase, those that are not separated by a complete number of wavelengths, are called out of phase. Examples of points like these would be A and C, or D and E, or B and H in the Activity. 5/ Period and Frequency Imagine you are sitting next to a pond and you watch the waves going past you. First one peak arrives, then a trough, and then another peak. Suppose you measure the time taken between one peak arriving and then the next. This time will be the same for any two successive peaks passing you. We call this time the period, and it is a characteristic of the wave. The symbol T is used to represent the period. The period is measured in seconds (s). Definition: The period (T) is the time taken for two successive peaks (or troughs) to pass a fixed point. Imagine the pond again. Just as a peak passes you, you start your stopwatch and count each peak going past. After 1 second you stop the clock and stop counting. The number of peaks that you have counted in the 1 second is the frequency of the wave. Definition: The frequency is the number of successive peaks (or troughs) passing a given point in 1 second. The frequency and the period are related to each other. As the period is the time taken for 1 peak to pass, then the number of peaks passing the point in 1 second is 1 T . But this is the frequency. So \[f = \dfrac{1}{T}\]or alternatively, \[T = \dfrac{1}{f}\]For example, if a wave takes 1/2s to go by then the period of the wave is 1/2s. Therefore, the frequency of the wave is: f = 1/T = 2 s−1 The unit of frequency is the Hertz (Hz) or s−1. Worked Example: Period and Frequency Question: What is the period of a wave of frequency 10 Hz? Answer Step 1 : Determine what is given and what is required We are required to calculate the period of a 10 Hz wave. Step 2 : Determine how to approach the problem We know that: T =1/f Step 3 : Solve the problem T = 1/f = 1/10 Hz= 0,1 s Step 4 : Write the answer The period of a 10 Hz wave is 0,1 s. 6/ Speed of a Transverse Wave The distance between two successive peaks is 1 wavelength, λ. Thus in a time of 1 period, the wave will travel 1 wavelength in distance. Thus the speed of the wave, v, is: However, f = 1/T. Therefore, we can also write: v = λ·f We call this equation the wave equation. To summarise, we have that v = λ · f where v = speed in m·s−1 λ = wavelength in m f = frequency in Hz Worked Example : Speed of a Transverse Wave 1 Question: When a particular string is vibrated at a frequency of 10 Hz, a transverse wave of wavelength 0,25 m is produced. Determine the speed of the wave as it travels along the string. Answer Step 1 : Determine what is given and what is required frequency of wave: f = 10 Hz wavelength of wave: λ = 0,25 m We are required to calculate the speed of the wave as it travels along the string. All quantities are in SI units. Step 2 : Determine how to approach the problem We know that the speed of a wave is: v = f · λ and we are given all the necessary quantities. Step 3 : Substituting in the values v = f · λ = (10 Hz)(0,25 m) = 2,5 m · s$^{−1}$ Step 4 : Write the final answer The wave travels at 2,5 m·s$^{−1}$ in the string. Exercise: Waves E - 1. List one property that distinguishes waves from matter. E - 2. When the particles of a medium move perpendicular to the direction of the wave motion, the wave is called a . . . . . . . . . wave. E - 3. A transverse wave is moving downwards. In what direction do the particles in the medium move? E - 4. Consider the diagram below and answer the questions that follow: (a) the wavelength of the wave is shown by letter . . . . . .. (b) the amplitude of the wave is shown by letter . . . . . .. E - 5. Draw 2 wavelengths of the following transverse waves on the same graph paper. Label all important values. (a) Wave 1: Amplitude = 1 cm, wavelength = 3 cm (b) Wave 2: Peak to trough distance (vertical) = 3 cm, peak to peak distance (horizontal) = 5 cm E - 6. You are given the transverse wave below. Draw the following: (a) A wave with twice the amplitude of the given wave. (b) A wave with half the amplitude of the given wave. (c) A wave with twice the frequency of the given wave. (d) A wave with half the frequency of the given wave. (e) A wave with twice the wavelength of the given wave. (f) A wave with half the wavelength of the given wave. (g) A wave with twice the period of the given wave. (h) A wave with half the period of the given wave. E - 7. A transverse wave with an amplitude of 5 cm has a frequency of 15 Hz. The horizontal distance from a crest to the nearest trough is measured to be 2,5 cm. Find the (a) period of the wave. (b) speed of the wave. E - 8. A fly flaps its wings back and forth 200 times each second. Calculate the period of a wing flap. E - 9. As the period of a wave increases, the frequency increases/decreases/does not change. E - 10. Calculate the frequency of rotation of the second hand on a clock. E - 11. Microwave ovens produce radiation with a frequency of 2 450 MHz (1 MHz =10$^{6 }$Hz) and a wavelength of 0,122 m. What is the wave speed of the radiation? E - 12. Study the following diagram and answer the questions: (a) Identify two sets of points that are in phase. (b) Identify two sets of points that are out of phase. (c) Identify any two points that would indicate a wavelength. E - 13. Tom is fishing from a pier and notices that four wave crests pass by in 8 s and estimates the distance between two successive crests is 4 m. The timing starts with the first crest and ends with the fourth. Calculate the speed of the wave. Xem thêm: Physics 10.V Transverse Wave High School Students Studying the Sciences Physics