Question

Question 1

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. she hears the shout 2.4 seconds after shouting. estimate the length of the lake.

Question 2

The A string on a violin has a fundamental frequency of 440 hz. the length of the vibrating portion is 33 cm and mass of .40 grams. Under what tension must the string be placed?\

Question 3
An organ pipe is 127 cm long. What are the fundamental overtones if the pipe is closed at one end.
F1_ f3__ f5__ f7
at open ends /
f1___ f2___ f3___ f4____

Answer 1

Number 1)

Apply d = vt (with only the time to go across)

d = (343)(1.2)

d = 411.6 m

Number 2)

Apply v = sqrt (T/u)

u = (4 X 10^-4)/(.33) = 1.21 X 10^-3

v = f(wavelength) = 440(2)(.33) = 290.4 m/s

290.4 = sqrt(T/1.21 X 10^-3)

T = 102 N

Number 3)

Closed Pipe

v = f(wavelength)

343 = f(4)(1.27)

f1 = 67.5 Hz =

f3 = 3f1 = 202.6 Hz

f5 = 5fi = 337.6 Hz

f7 = 7f1 = 472.6 Hz

Open Pipe

v = f(wavelength)

343 = f(2)(1.27)

f1 = 135 Hz

f2 = 2f1 = 270 Hz

f3 = 3f1 = 405.1 Hz

f4 = 4f1 = 540.2 Hz