Question

A bat emits ultrasonic sound of frequency 100 K Hz in air. If this sound meets a water surface, what is the wavelength of the reflected sound speed of sound in air = 340 ms^-1 and in water = 1486 ms^-1.

Answer 1

The wavelength of the reflected sound can be calculated using the formula: wavelength = velocity / frequency.

Given:

Frequency of the ultrasonic sound emitted by the bat = 100 kHz (100,000 Hz)

Speed of sound in air = 340 m/s

Speed of sound in water = 1486 m/s

To find the wavelength of the reflected sound, we need to calculate the velocity of the sound in water.

Using the formula: velocity = wavelength x frequency, we can rearrange it to solve for wavelength.

wavelength = velocity / frequency

In air:

wavelength in air = velocity in air / frequency

wavelength in air = 340 m/s / 100,000 Hz

Now, let's find the velocity of the sound in water:

velocity in water = wavelength in air x frequency

velocity in water = wavelength in air x 100,000 Hz

velocity in water = wavelength in air x 100,000 Hz

Finally, we can find the wavelength of the reflected sound:

wavelength of the reflected sound = velocity in water / frequency

Substituting the values, we get:

wavelength of the reflected sound = (wavelength in air x 100,000 Hz) / 100,000 Hz

Simplifying the equation, we find:

wavelength of the reflected sound = wavelength in air

Therefore, the wavelength of the reflected sound is equal to the wavelength in air.