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2. Mac and Tosh stand 8 meters apart and demonstrate the motion of a transverse wave on a snakey. The wave e can be described as having a vertical distance of 32 cm from a trough to a crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to the nearest trough. Determine the amplitude, period, and wavelength and speed of such a wave.

Amplitude = 16 cm (Amplitude is the distance from the rest position to the crest position which is half the vertical distance from a trough to a crest.) Wavelength = 96 cm (Wavelength is the distance from crest to crest, which is twice the horizontal distance from crest to nearest trough.) Period = 0.42 s (The period is the reciprocal of the frequency. T = 1 / f) Speed = 230 cm/s (The speed of a wave is calculated as the product of the frequency times the wavelength.)

3. Dawn and Aram have stretched a slinky between them and begin experimenting with waves. As the frequency of the waves is doubled, a. the wavelength is halved and the speed remains constant b. the wavelength remains constant and the speed is doubled c. both the wavelength and the speed are halved. d. both the wavelength and the speed remain constant.

Answer: A Doubling the frequency will not alter the wave speed. Rather, it will halve the wavelength. Wavelength and frequency are inversely related.

2. As the wavelength of a wave in a uniform medium increases, its frequency will _____. a. decrease b. increase c. remain the same

Answer: A In rows 1 and 2, the wavelength was increased and the frequency was decreased. Wavelength and frequency are inversely proportional to each other.

3. The speed of a wave depends upon (i.e., is causally affected by) ... a. the properties of the medium through which the wave travels b. the wavelength of the wave. c. the frequency of the wave. d. both the wavelength and the frequency of the wave.

Answer: A Whenever the medium is the same, the speed of the wave is the same. However, when the medium changes, the speed changes. The speed of these waves were dependent upon the properties of the medium.

1. Two waves on identical strings have frequencies in a ratio of 2 to 1. If their wave speeds are the same, then how do their wavelengths compare? a. 2:1 b. 1:2 c. 4:1 d. 1:4

Answer: B Frequency and wavelength are inversely proportional to each other. The wave with the greatest frequency has the shortest wavelength. Twice the frequency means one-half the wavelength. For this reason, the wavelength ratio is the inverse of the frequency ratio.

1. As the wavelength of a wave in a uniform medium increases, its speed will _____. a. decrease b. increase c. remain the same

Answer: C In rows 1 and 2, the wavelength was altered but the speed remained the same. The same can be said about rows 3 and 4 and rows 5 and 6. The speed of a wave is not affected by the wavelength of the wave.

4. A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second. a. What is the frequency in Hertz of the sound wave? b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

Answer: f = 70 Hz and λ = 5.0 m The frequency is given and the wavelength is the v/f ratio.

6. Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position every 3 seconds. When one is up the other is down. There are never any wave crests between the boats. Calculate the speed of the waves.

The diagram is helpful. The wavelength must be 8 meters (see diagram). The period is 3 seconds so the frequency is 1 / T or 0.333 Hz. Now use speed = f • wavelength Substituting and solving for v, you will get 2.67 m/s.

5. Ocean waves are observed to travel along the water surface during a developing storm. A Coast Guard weather station observes that there is a vertical distance from high point to low point of 4.6 meters and a horizontal distance of 8.6 meters between adjacent crests. The waves splash into the station once every 6.2 seconds. Determine the frequency and the speed of these waves.

The wavelength is 8.6 meters and the period is 6.2 seconds. The frequency can be determined from the period. If T = 6.2 s, then f =1 /T = 1 / (6.2 s) f = 0.161 Hz Now find speed using the v = f • λ equation. v = f • λ = (0.161 Hz) • (8.6 m) v = 1.4 m/s