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 0.697 m from its equilibrium position and then releasing it. The force constant for the spring is

k = 46.8 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 345 Hz. If your lab partner Pat stands at the end of the air track, determine the highest and lowest frequencies she hears. The speed of sound in air is 343 m/s. (Enter your answers to at least the nearest Hz.)

Explanation / Answer

We first need to find the max speed of the system from conservation of energy

PE = KE

.5kx2 = .5mv2

(46.8)(.697)2 = (4)(v2)

v = 2.384 m/s

Then by the Doppler Effect...

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

For the highest frequecny...

f' = 345(343/343-2.384)

f' = 347.4 Hz

For the lowest frequency...

f' = 345(343/343+2.384)

f' = 342.6 Hz

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