You attach a speaker to an air track cart and then attach the cart to one end of

Question

You attach a speaker to an air track cart and then attach the cart to one end of the air track by means of a spring and start the system oscillating by stretching the spring 0.797 m from its equilibrium position and then releasing it. The force constant for the spring is k = 49.8 N/m, the total mass of the speaker and air track cart are 4.00 kg, and the speaker emits sound with a frequency of 405 Hz. If your lab partner Hal stands at the end of the air track, determine the highest and lowest frequencies he hears. The speed of sound in air is 343 m/s. (Enter answers to at least the nearest Hz.)

Lowest Frequency =

Highest Freqency =

Explanation / Answer

We need the max speed of the spring system

Apply PE = KE

.5kx^2 = .5mv^2

(.5)(49.8)(.797)^2 = (.5)(4)(v^2)

v = 2.81 m/s

Now apply the Doppler effect for the maximum

f = f'(v)/(v-vs)

f = (405)(343)/(343-2.81)

f = 408.3 Hz

For the minimum

f = f'(v)/(v-vs)

f = (405)(343)/(343+2.81)

f = 401.7 Hz

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