2. A 14 kg hanging sculpture is suspended by a 85-cm-long, 4.0 g steel wire. Whe
ID: 1455965 • Letter: 2
Question
2. A 14 kg hanging sculpture is suspended by a 85-cm-long, 4.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency.
What is the frequency of the hum?
3. An ultrasound unit is being used to measure a patient's heartbeat by combining the emitted 2.0 MHz signal with the sound waves reflected from the moving tissue of one point on the heart. The beat frequency between the two signals has a maximum value of 500 Hz .
What is the maximum speed of the heart tissue? The speed of ultrasound waves in human tissue is 1540 m/s.
Explanation / Answer
3.
f = frequency of signal = 2 x 106 Hz
Vs = speed of ultrasound waves = 1540 m/s
Vh = speed of heat tissue
when signal moves towards the tissue , heat behaves as observer and machine as source
frequency observed by the hert is given as
f' = (Vs + Vh ) f / Vh
f' = (1540 + Vh) ( 2 x 106 ) /Vh eq-1
after reflection
Heat behaves as source and machine as observer
frequency observed by the machine is given as
f'' = Vh f' / (Vs - Vh)
Beat frequency is given as
beat frequency = f - f'' = f - Vs f' / (Vs - Vh)
Beat frequency = f - Vh f' / (Vs - Vh) = f - Vh / (Vs - Vh) ((1540 + Vh) ( f) /Vh ) = 2 Vh f / (Vs - Vh)
500 = 2 Vh (2 x 106) / (1540 - Vh)
Vh = 0.192 m/s
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