# Transverse waves – problems and solutions

1. The distance between the two troughs of the water surface waves is 20 m. An object floats on the surface of the water so that it experiences the vibration motion. If the time to travel one vibration is 4 seconds, then the velocity of wave is …. m/s

A. 20

B. 15

C. 10

D. 5

__Known :__

Wavelength (λ) = 20 meters

Period (T) = 4 seconds

__Wanted:__ Speed of wave (v)

__Solution :__

The equation of the speed of wave :

v = λ / T = 20 meters / 4 seconds = 5 meters / second

The correct answer is D.

2. Two points A and B are on the rope and are 90 cm apart from one another. On the rope propagates the transverse waves, so that point A is at the top of the wave, point B at the bottom of the wave, and between them, there are two crests and two troughs. If the wave period is 0.3 seconds, then the wave propagation is…

A. 10.8 cm/s

B. 18.0 cm/s

C. 120.0 cm/s

D. 200.0 cm/s

__Known :__

Distance AB (l) = 90 cm

Period of wave (T) = 0.3 seconds

Frequency of wave (f) = 1/0.3 seconds

Point A is at crest of wave and point B is at trough of wave.

Between point A and B, there are two crests and two troughs.

__Wanted :__ Speed of wave (v = f λ)

__Solution :__

Based on figure, can concluded there are 2.5 wavelengths. Distance of a wavelength (λ) = 90 cm / 2.5 = 36 cm

The speed of wave :

v = f λ = (1 / 0.3)(36) = 36 / 0.3 = 120 cm/s.

The correct answer is C.

3. The following graph displays the displacement of a point in one medium as a function of time when a wave passes through the medium.

If the wavelength is 6 meters, then the speed of the wave propagation is…

A. 3 m/s

B. 6 m/s

C. 8 m/s

D. 12 m/s

__Known :__

There are two wavelengths based on the graph above.

Distance of 1 wavelength (λ) = 6 meters / 2 = 3 meters

Period (T) = 0.5 seconds

__Wanted :__ Speed of waves (v)

__Solution :__

v = f λ = λ / T = 3 meters / 0.5 seconds = 6 meters / second

The correct answer is B.

4. Based on figure below, the point that has phase difference ¾ with point A is ….

A. Point B

B. Point C

C. Point D

D. Point E

Solution

Point B has a phase difference of ¼ λ with point A

Point C has a phase difference of 2/4 λ or 1/2 λ with point A

Point D has a phase difference of 3/4 λ with point A

Point F has a phase difference of 5/4 λ with point A.

The correct answer is C.

5. On a pond’s surface, there are two dry leaves 60 centimeters away from each other. Both move up and down like the surface of the water with a frequency of 2 Hz. When one leaf is at the crest, the other leaves are at the trough, and between them, there is one crest and one trough. Determine the speed of the wave propagation of the wave.

A. 20 cm/s

B. 30 cm/s

C. 80 cm/s

D. 120 cm/s

__Known :__

Distance between both leaves = 60 cm

Frequency (f) = 2 Hz = 2

__Wanted :__ The speed of wave

__Solution :__

Between both leaves there are 1.5 wavelength. Distance of 1 wavelength is (λ) = 60 cm / 1.5 = 40 cm

Speed of wave (v) :

v = f λ = (2 hz)(40 cm) = 80 cm/second

The correct answer is C.

6. Based on figure below, determine the amplitude, period, frequency and speed of the wave.

Solution :

Amplitude (A) = 4 meters

Period (T) = 6 seconds / 3 = 2 seconds

Frequency (f) = 1 / T = 1 / 2 = 0.5 hertz

Wavelength (λ) = 24 meters / 3 = 8 meters

Speed of wave (v) = f λ = (0.5 hertz)(8 meters) = 4 meters/second or

Speed of wave (v) = λ / T = 8 meters / 2 second = 4 meters/second

The correct answer is D.

7. On a string with length of 1.2 m and mass of 200 g formed 1.5 sinusoidal waves with frequency of 50 Hz. Based on these data, determine the wave period and the tension force of the rope.

A. Period = 0.02 seconds and tension force = 6.67 N

B. Period = 0.01 seconds and tension force = 6.67 N

C. Period = 0.02 seconds and tension force = 266.67 N

D. Period = 0.01 seconds and tension force = 266.67 N

__Known :__

Length of rope (l) = 1.2 meters and there are 1.5 sinusoidal waves so that distance of 1 wavelength (λ) = 1.2 meters / 1.5 = 0.8 meters

Mass of rope (m) = 200 gram = 0.2 kg

Frequency (f) = 50 Hz

Density of rope (µ) = m/l = 0.2 kg / 1.2 meters = (1/6) kg/meter

__Wanted :__ Period of wave (T) and the tension force of rope (T)

__Solution :__

Period of wave :

T = 1 / f = 1 / 50 Hz = 0.02 seconds

The speed of wave on rope :

v = f λ = (50 hz)(0.8 meters) = 40 meters/second

The tension force (T) :

The correct answer is C.