Sound waves of a certain frequency in air having a wavelength of 1.9 m will have what wavelength in water? Take the speed of sound in air to be 340 m/s and in water to be 1 490 m/s.
A)0.57 m
B)1.9 m
C)8.3 m
D)11 m

Question

Quizplus · Accepted Answer

The formula relating wavelength, frequency, and speed is: λ = v/f
Using this formula with the given values, we get:
λ_air = v_air/f = 340 m/s / (f_air)
λ_water = v_water/f = 1490 m/s / (f_water)
Since the frequency is the same for both air and water, we can set the two equations equal to each other and solve for λ_water:
λ_air = λ_water
v_air/f_air = v_water/f_water
f_water = (v_water/v_air) * f_air
λ_water = v_water/f_water = v_water/[(v_water/v_air) * f_air] = (v_air/v_water) * λ_air
Plugging in the given values, we get:
λ_water = (340 m/s)/(1490 m/s) * 1.9 m ≈ 0.44 m
Therefore, the closest answer choice is C) 8.3 m.

Sound Waves of a Certain Frequency in Air Having a Wavelength