A certain sound has a wavelength of 1.70m in the air. The speed of sound in water is 1.45x10³m/s. The speed of sound in steel is 5.00x10³m/s.
a) What is the wavelength in water for the sound which has a wavelength of 1.70m in the air?
b) What is the wavelength of this sound in steel?
The wave equation: freq*wavelength=speed
a) You are going to have to assume a speed of sound in air: 335m/s
wavelengthwater= wavelengthair*speedwater/speedair
= 1.70*1.45e3/335= 7,35 m
b. wavelengthsteel=1.70*5e3/335=25m
so as speed goes up, wavelength gets longer
To answer these questions, we can use the formula:
Wavelength = Speed of Sound / Frequency
However, we are not given the frequency of the sound, so we need to find it first. The frequency remains the same as the sound passes through different mediums, so we can use the wavelength in air to find the frequency.
a) To calculate the wavelength in water, we need to use the speed of sound in water and the frequency in air.
Using the formula: Speed in air = Speed in water
So, the frequency in air is the same as the frequency in water.
Now, let's calculate the frequency in air using the given wavelength in air:
Wavelength in air = 1.70 m
Frequency = Speed of Sound in air / Wavelength in air
Frequency = Speed of Sound in air / 1.70 m
Substituting the given values:
Frequency = Speed of Sound in air / 1.70 m
Frequency = Unknown / 1.70 m
Since we are only interested in finding the ratio and not the actual value of frequency, we can assume it as Unknown.
Now, let's calculate the wavelength in water using the frequency as Unknown:
Wavelength in water = Speed of Sound in water / Frequency
Wavelength in water = 1.45x10³ m/s / Unknown
b) Similarly, to find the wavelength in steel, we can use the speed of sound in steel with the frequency. Since the frequency remains the same, we can use the Unknown frequency obtained in part a.
Wavelength in steel = Speed of Sound in steel / Frequency
Wavelength in steel = 5.00x10³ m/s / Unknown
So, to summarize:
a) The wavelength in water for the sound with a wavelength of 1.70 m in air is 1.45x10³ m/s / Unknown.
b) The wavelength of this sound in steel is 5.00x10³ m/s / Unknown.