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You ride your bike at 10.7 m/s directly away from your neighbor's trumpet sound and toward the sound of another neighbor's trombone and find that you hear both instruments at exactly the same pitch. The trumpeter is practicing her middle Cat a frequency of 262 Hz What frequency is the trombonist producing? The speed of sound in air is 337 m/s.

Respuesta :

Answer:

The frequency of the trombonist producing is 245.87 Hz.

Explanation:

Given that,

Frequency = 262 Hz

Speed of sound = 337 m/s

Speed = 10.7

We need to calculate the frequency for the trumpet

Using Doppler effect

[tex]f'=f\dfrac{v-v_{s}}{v}[/tex]

Where, v = speed of sound

[tex]v_{s}[/tex] = speed of source

f = frequency

Put the value into the formula

[tex]f'=\dfrac{262\times(337-10.7)}{337}[/tex]

[tex]f'=253.68\ Hz[/tex]

We need to calculate the frequency for the trombonist

Using formula of frequency again

[tex]f'=f\dfrac{v+v_{s}}{v}[/tex]

Put the value into the formula

[tex]253.68=\dfrac{f(337+10.7)}{337}[/tex]

[tex]f=\dfrac{253.68\times337}{347.7}[/tex]

[tex]f=245.87\ Hz[/tex]

Hence, The frequency of the trombonist producing is 245.87 Hz.

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