PHYSICS 2053A PROBLEMs: 5 points each part Show your work, and clearly indicate

Question

PHYSICS 2053A PROBLEMs: 5 points each part Show your work, and clearly indicate your final answer. You may attach additional pages or use the backs of these. Remember to employ appropriate significant figures and units! 1) A guitar string of length 0.500 m and a mass of 40.0 grams is held with a tension of 5.00x 10 N. It is plucked so as to excite the fundamental frequency alone A) What is the velocity of the wave on the string? What is the frequency and wavelength of the fundamental (first) harmonic? B) The vibrating string gives rise to a sound wave in the air with the same frequency. What is the wavelength of this sound wave? You may assume a speed of sound in air of 335.0 m/s. C) The guitar body rests 40 cm from the player's ear. What is the difference in the intensity levels heard by the guitar player and a listener 6.0 meters away?

Explanation / Answer

1. (A) v = sqrt[ T / linear mass density ]

v = sqrt[ 5000 / (0.040/0.5)]

v = 250 m/s ......Ans

for first harmonic (fundamental),

wavelength = 2 L = 1 m ......Ans

f = v / wavelength = 250 Hz ......Ans

(B) f will be same. f = 250 Hz

v = 335 m/s

wavelength = v /f = 1.34 m  

(c) I = 10 log(I / I0)

and I = P / (4 pi r^2)

I1 - I2 = 10 log (I1 / I2) = 10 log(r2^2 / r1^2)

= 20 log(6/0.40)

= 47 dB

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