You ride your bike at 12.1 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 C at a frequency of 262 Hz . What frequency is the trombonist producing? The speed of sound in air is 337 m/s .

243.83 Hz

Explanation:

Given the following :

Recall :

When source is stationary and observe is in motion:

Moving away from the source :

Observed frequency f₀ = f(v-v₀/v)

Moving towards the source :

f₀ = f(v+v₀/v)

Hence ;

v₀ = 12.1 m/s ; f of trumpeter = 262 Hz ; speed of sound (v) = 337m/s

f(v+v₀/v) = 262(v-v₀/v)

f = 262(v-v₀/v) / (v+v₀/v)

f = 262(v-v₀/v) * (v / v+v₀)

f = 262 (v-v₀ / v+v₀)

f = 262 ((337 - 12.1) / (337 + 12.1))

f = 262 (324.9 / 349.1)

f = 262 (0.93067888857)

f = 243.83

f = 244Hz

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