A dog can hear sounds in the range from 15 to 50,000 Hz. What wavelength corresponds to the upper cut-off point of the sounds at 20◦C where the sound speed is 344 m/s? Answer in units of m.

Give that,

The frequency range the dog can hear is 15Hz to 50,000Hz

The wavelength of sound in air at 20°C =?

Speed of sound is 344

The frequency corresponding to the lower cut-off point is the lowest frequency which his 15Hz

F=15Hz

The relationship between the wavelength, speed and frequency is given as

v=fλ

Then,

λ=v/f

λ=v/f

λ=344/15

λ=22.93m

The wavelength corresponds to the upper cut-off point of the sounds at 20◦C is 0.00688m

Explanation:

The wavelength, velocity and the frequency of a wave can be expressed using the relationship;

v = f¶ where;

v is the velocity of the wave

f is the frequency of the wave

¶ is the wavelength

Given;

v = 344m/s

If the dog can hear sounds in the range from 15 to 50,000, maximum frequency the dog can hear will be 50,000Hz

Since we are to find the wavelength that corresponds to the upper cut-off point of the sounds, our value of the frequency will be the maximum frequency which is 50,000Hz

f = 50,000Hz

From the formula above;

¶ = v/f

¶ = 344/50,000

¶ = 0.00688m

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