You are driving along the highway at 30 m/s through still air at 25 Celsius chas

Question

You are driving along the highway at 30 m/s through still air at 25 Celsius chasing an unidentified flying object traveling away from you with a ground speed of 100 m/s. The alien life forms within the ship begin playing a steel piano wire that is 1.5 m long; and, has a mass per unit length of 0.009 kg/m. The tension in the wire is 9000 N.

a. What is the wave propagation speed on the wire?

b. What is the wavelength of the fundamental?

c. What is the fundamental frequency of the wire on board the ship?

d. If that fundamental frequency is the same as the audible frequency that the UFO emits, what frequency do you hear in your automobile?

Explanation / Answer

part a:

speed of wave propagation on a string=sqrt(tension/mass per unit length)

=sqrt(9000/0.009)=1000 m/s

b) then fundamental frequency=speed of wave/(2*length)

=1000/(2*1.5)=333.33 Hz

as speed of the wave=frequency*wavelength

==>wavelength of fundamental frequency=speed/frequency

=1000/333.33

=3 m

c)fundamental frequency=333.33 Hz

d)using doppler effect,

the freqeuncy heard by a stationary observer is given by

f=f0*(u+v1)/(u+v2)

where f0=original frequency emitted=333.33 Hz

u=speed of sound in air=343 m/s

v1=speed of the receiver, positive if receiver is moving towards the source

here v1=30 m/s
v2=speed of the source , positive if source is moving away from the receiver

=100 m/s

then frequency heard by you=333.33*(343+30)/(343+100)=280.662 Hz

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.