A student is comparing the speed of sound in air and water. She measures the frequency, f, and wavelength, λ, of sound waves in both air and water. The results are shown in the following table. Based on her data, how does the speed of sound in water compare to the speed of sound in air? A. The speed of sound through water is 4.3 times faster than sound through air.
B. The speed of sound through water is 2.6 times slower than sound through air.
C. The speed of sound through water is 8.4 times faster than sound through air.
D. The speed of sound through air is approximately equal to the speed of sound through water.

Option A. The speed of sound through water is 4.3 times faster than sound through air.

Explanation:

To answer the question correctly, we shall determine the speed of the wave in both cases. This is illustrated below:

For Air:

Frequency (fₐ) = 195 Hz

Wavelength (λₐ) = 1.76 m

Velocity (vₐ) =?

vₐ = λₐfₐ

vₐ = 1.76 × 195

vₐ = 343.2 m/s

For Water:

Frequency (fᵥᵥ) = 195 Hz

Wavelength (λᵥᵥ) = 7.6 m

Velocity (vᵥᵥ) =?

vᵥᵥ = λᵥᵥfᵥᵥ

vᵥᵥ = 7.6 × 195

vᵥᵥ = 1482 m/s

Finally, we shall compare the speed in water to that of air. This can be obtained as follow:

Velocity in air (vₐ) = 343.2 m/s

Velocity in water (vᵥᵥ) = 1482 m/s

Water : Air

vᵥᵥ : vₐ =>

vᵥᵥ / vₐ = 1482 / 343.2

vᵥᵥ / vₐ = 4.3

Cross multiply

vᵥᵥ = 4.3 × vₐ

Thus, the speed in water is 4.3 times the speed in air.

Option A gives the correct answer to the question.

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