4.6- MORE ABOUT STATIONARY WAVES

Question 1

What can be the controlled arrangement for producing stationary waves? (stationary waves on a vibrating string)

Answer 1

string/ wire tied at one end to mechanical vibrator connected to frequency generator

other end of string passes over pulley + supports a weight, which keeps tension in string constant

Question 2

What happens when the frequency is increased? (stationary waves on a vibrating string)

Answer 2

different stationary wave patterns seen on string

Question 3

What does the length of string between the pulley + vibrator have at either end? (stationary waves on a vibrating string)

Answer 3

node at either end

Question 4

At what frequency is the first harmonic pattern of vibration seen? (stationary waves on a vibrating string)

Answer 4

seen at lowest possible frequency that gives a pattern

Question 5

Where is the antinode and nodes on the first harmonic pattern of vibration? (stationary waves on a vibrating string)

Answer 5

antinode in middle + node at either end

Question 6

What is the equation for the first harmonic wavelength?λ

Answer 6

λ1 = 2L

L- length

Question 7

What is the equation for the first harmonic frequency? (stationary waves on a vibrating string)

Answer 7

f = c = c
– —
λ1 2L

c- speed of progressive waves on wire

Question 8

Where is the node in the second harmonic?

Answer 8

node at the middle

Question 9

As there is a node in the middle of the second harmonic, how many loops are there?

Answer 9

string is in two loops

Question 10

What is the wavelength of the second harmonic?

Answer 10

λ2 = L

Question 11

What is the frequency of the second harmonic vibrations?

Answer 11

f2 = c = c = 2f1
— —
λ2 L

Question 12

Where is the nodes and antinodes in the third harmonic?

Answer 12

nodes at distance of 1/3L from either end and an antinode at the middle

Question 13

What is the frequency of the third harmonic vibration?

Answer 13

f3 = c = 3c = 3f1
— —-
λ3 2L

Question 14

In general at what frequencies do stationary wave patterns occur?

Answer 14

f1, 2f1, 3f1, 4f1 etc.

f- first harmonic frequency of the fundamental vibrations

Question 15

What happens to the progressive wave sent out by the vibrator? (explanation of the stationary waves patterns on a vibrating string)

Answer 15

crest reverses its phase when it reflects at the fixed end + travels back along the string as a trough

Question 16

What happens to the progressive wave when it reaches the vibrator when it was reversed? (explanation of the stationary waves patterns on a vibrating string)

Answer 16

it reflects and reverses phase again, travelling away from the vibrator once more as a crest

Question 17

How can the crest of the progressive wave be reinforced and

what happens to amplitude

what does this form? (explanation of the stationary waves patterns on a vibrating string)

Answer 17

by a crest created by the vibrator

amplitude of wave increased

this is how stationary wave formed

Question 18

What is the key condition for stationary waves to be formed? (explanation of the stationary waves patterns on a vibrating string)

Answer 18

time taken for wave to travel along string and back should be equal to time taken for whole number of cycles of vibrator

Question 19

What is the equation for the time taken for a wave to travel along the string and back?

Answer 19

t = 2L/c

c- speed of waves on string

Question 20

What is the equation for the time taken vibrator to pass through a whole number of cycles?

Answer 20

m/f

f- frequency
m- whole number

Question 21

What can the key condition for the formation of a stationary wave be expresses as? (explanation of the stationary waves patterns on a vibrating string)

Answer 21

2L/c = m/f

Question 22

At what frequencies are stationary waves formed?

Answer 22

f, 2f, 3f, etc

Question 23

What is the equation for the length of the vibrating section of the string?

Answer 23

L = mλ/2 = whole number of half wavelengths

Question 24

What does the pitch of a note correspond to?

Answer 24

frequency

Question 25

How can the pitch of a note from a stretched string be altered?

Answer 25

by changing the tension of the string or by altering its length

Question 26

What does raising the tension do to the pitch?

Answer 26

increases pitch

Question 27

What does shortening the length do to the pitch?

Answer 27

increase pitch

Question 28

What does lowering the tension do the pitch?

Answer 28

lowers the pitch

Question 29

What does increasing the length do to the pitch?

Answer 29

lowers the pitch

Question 30

How can a vibrating string/ wire be tuned to the same pitch as a tuning fork?

Answer 30

by changing the length or altering the tension

Question 31

What is the difference between a vibrating string and tuning fork? (hint- frequencies)

Answer 31

sound from a vibrating string includes all the harmonic frequencies, whereas a tuning fork vibrates only at a single frequency

Question 32

When is a wire tuned?

Answer 32

when its first harmonic frequency is the same as the tuning fork frequency

Question 33

Equation for the first harmonic frequency

Answer 33

f = 1 root T/ µ
—-
2L

T- tension
µ- mass per unit length

Question 34

What is a simple visual check when using a tuning fork to tune a wire?

Answer 34

balance a small piece of paper on the wire as its centre

placing the base of the vibrating tuning fork on one end of the wire will cause the paper to fall off if the wire is tuned correctly