A sound wave travels in air toward the surface of a freshwater lake and enters into the water. The frequency of the sound does not change when the sound enters the water. The wavelength of the sound is 3.52 m in the air, and the temperature of both the air and the water is 20 oC. What is the wavelength in the water?
Pls help!
distance = speed * time
here time is the period, T, which is 1/f and constant if f is constant which they did not have to tell us because we know there is no place to store extra waves.
distance is the wavelength or how far it goes in time T
so
lambda = V T
3.52 = Vair T
so
T = (3.52/Vair)
same T in water so
(3.52/Vair) = x / Vwater
solve for x
What do I use as the speed of water and air?
Va = 330 m/s.
Vw = 1490 m/s.
3.52 = Va/F
3.52 = 330/F,
F = 93.75 Hz.
Wavelength = Vw/F = 1490/93.75 = 15.89 m.
To find the wavelength of the sound wave in water, we can use the equation:
wavelength in water = wavelength in air / (velocity of sound in water / velocity of sound in air)
First, let's find the velocity of sound in air at 20 oC. We can use the approximate formula:
velocity of sound in air = 331.5 m/s + (0.6 m/s/°C) * temperature in Celsius
Plugging in the given temperature:
velocity of sound in air = 331.5 m/s + (0.6 m/s/°C) * 20 oC
= 331.5 m/s + 12 m/s
= 343.5 m/s
Next, let's find the velocity of sound in water at 20 oC. We can use the formula:
velocity of sound in water = 1481 m/s + (4.7 m/s/°C) * temperature in Celsius
Plugging in the given temperature:
velocity of sound in water = 1481 m/s + (4.7 m/s/°C) * 20 oC
= 1481 m/s + 94 m/s
= 1575 m/s
Now, we can calculate the wavelength in the water using the formula mentioned earlier:
wavelength in water = 3.52 m / (1575 m/s / 343.5 m/s)
= 3.52 m / 4.5812
≈ 0.767 m
Therefore, the wavelength of the sound wave in water is approximately 0.767 meters.