4.6 More about stationary waves on strings

Question 1

Controlled arrangement for producing stationary waves

Answer 1

Frequency generator connected to vibrator (nearly at a node), string from vibrator over a pulley. hang weights on the end to keep the tension in the string constant. As the frequency of the generator increases from a very low value, different stationary wave patterns are seen on the string

Question 2

The wavelength of the waves that form the pattern of the first harmonic is

Answer 2

λ 1 = 2L

Question 3

What is the frequency of the first harmonic

Answer 3

f1=c/λ1 =c/2L

Question 4

Describe the pattern of the first harmonic

Answer 4

Seen at the lowest possible frequency that gives a pattern. Has an antinode in the middle and two nodes at either end. Distance between nodes=1/2λ 1

Question 5

Describe the pattern of the second harmonic

Answer 5

There are two nodes at either end, and one in the middle, so there are two loops. Each loop has a length of half a wavelength

Question 6

The wavelength of the waves that form the pattern of the first harmonic is

Answer 6

λ 2 = L

Question 7

What is the frequency of the second harmonic

Answer 7

f2=c/λ 2 = c/L = 2f1

Question 8

Describe the pattern of the third harmonic

Answer 8

Two nodes at either end and two in between, the distance between each node is 1/3L. There are three antinodes.

Question 9

The wavelength of the waves that form the pattern of the third harmonic is

Answer 9

λ 3 = 2/3L

Question 10

What is the frequency of the third harmonic

Answer 10

f3=c/λ 3 = 3c/2L = 3f1

Question 11

In general, stationary wave patterns occur aat frequencies f1, 2f1, 3f1, 4f1 etc. where f is the _______ ______ frequency of the ______ vibrations. This is the case in any vibrating linear system that has a node at either end

Answer 11

First harmonic

Fundamental

Question 12

What happens to a progressive wave sent out by the vibrator in the setup with the string, pulley and weights

Answer 12

The crest reverses its phase when it reflects at the fixed end and travels back along the string as a trough. When it reaches the vibrator, it reflects and reverses phase again, travelling away from the vibrator once more as a crest. If this crest is reinforced by a crest created bu the vibrator, the amplitude of the wave is increased

Question 13

The time taken for a wave to travel along the sting and back is:

Answer 13

t=2L/c

Where c is the speed of the wave on the string

Question 14

The time taken for the vibrater to pass through a whole number of cycles =

Answer 14

m/f

Where f is the frequency of the vibrator and m is a whole number

Question 15

The length of the vibrating section of a string L

Answer 15

L=mλ/2 = a whole number of half wavelengths

Question 16

What does the pitch of a note correspond with

Answer 16

Frequency

Question 17

How to change the pitch on a string

Answer 17

Change the tension
Raising the tension or shorten the length increases the pitch.
Lowering the tension or increasing the length lowers the pitch

Question 18

What is the difference in sound between a tuning fork and a piece of string

Answer 18

A string includes all the harmonic frequencies whereas a tuning fork vibrates only at a single frequency

Question 19

It can be shown that the first harmonic frequency f depends on the tension T in the wire and its mass per unit length μ

Answer 19

f=1/2L root T/μ