Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. A pipe closed at both ends can have standing waves inside of it, but you normally don’t hear them because little of the sound can get out. But you can hear them if you are inside the pipe, such as someone singing in the shower. (a) Show that the wavelengths of standing waves in a pipe of length L that is closed at both ends are λn=2L/n and the frequencies are given by fn=nv/2L=nf1, where n=1,2,3,… (b) Modeling it as a pipe, find the frequency of the fundamental and the first two overtones for a shower 2.50 m tall. Are these frequencies audible?

68.8 Hz

137.6 Hz, 206.4 Hz

Explanation:

L = Length of tube = 2.5 m

v = Velocity of sound in air = 344 m/s

Distance between nodes is given by

Where n = 0, 1, 2, 3, ...

Making n+1 = n

where n = 1, 2, 3 .....

For fundamental frequency n = 1

Frequency is given by

The fundamental frequency is 68.8 Hz

First overtone

Second overtone

The overtones are 137.6 Hz, 206.4 Hz

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards

float.

archimedes' principle

denser than water sinks in water.

denser than mercury would sink in it