A guitar string attached at both ends is 40 cm long and produces a fundamental n

Question

A guitar string attached at both ends is 40 cm long and produces a fundamental note of frequency 200 Hz wen plucked. What are the frequencies of the second and third overtones of this string?

A. 300 and 400 Hz

B. 100 and 200 Hz

C. 200 and 400 Hz

D. 400 and 600 Hz

E. 400 and 800 Hz

Four waves are described by the following equations, where the distances are measured in meters and time in seconds; Which of these waves are moving with the same speed?

i. y=0.12cos(3x-21t)

ii. y=0.15cos(6x+42)

iii.y=0.13cos(6x+21t)

iv. y= -0.23cos(3x-42t)

A. ii and iii.

B. ii and ic

C. iii and ic

D. i and ii

E. i and iii

Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?

A. T(sqrt2)

B. T

C. 2T

D. T/ (sqrt2)

E. T/2

Explanation / Answer

Second overtone is the third harmonic, hence has frquency

F = 3f= 600 Hz

For third vertone

F = 4f = 800 hz (These are not given as the options, !)

2) option D as 1 and 2 are moving at same speed

Speed = w/k

for 1 Speed = 21/3 = 7

for 2 speed = 42/6 = 7

3) We know T = sqrt(L/g)

Hence time period is independent of mass , so both will have the same time period

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