4.6- MORE ABOUT STATIONARY WAVES Flashcards
What can be the controlled arrangement for producing stationary waves? (stationary waves on a vibrating string)
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
What happens when the frequency is increased? (stationary waves on a vibrating string)
different stationary wave patterns seen on string
What does the length of string between the pulley + vibrator have at either end? (stationary waves on a vibrating string)
node at either end
At what frequency is the first harmonic pattern of vibration seen? (stationary waves on a vibrating string)
seen at lowest possible frequency that gives a pattern
Where is the antinode and nodes on the first harmonic pattern of vibration? (stationary waves on a vibrating string)
antinode in middle + node at either end
What is the equation for the first harmonic wavelength?λ
λ1 = 2L
L- length
What is the equation for the first harmonic frequency? (stationary waves on a vibrating string)
f = c = c
– —
λ1 2L
c- speed of progressive waves on wire
Where is the node in the second harmonic?
node at the middle
As there is a node in the middle of the second harmonic, how many loops are there?
string is in two loops
What is the wavelength of the second harmonic?
λ2 = L
What is the frequency of the second harmonic vibrations?
f2 = c = c = 2f1
— —
λ2 L
Where is the nodes and antinodes in the third harmonic?
nodes at distance of 1/3L from either end and an antinode at the middle
What is the frequency of the third harmonic vibration?
f3 = c = 3c = 3f1
— —-
λ3 2L
In general at what frequencies do stationary wave patterns occur?
f1, 2f1, 3f1, 4f1 etc.
f- first harmonic frequency of the fundamental vibrations
What happens to the progressive wave sent out by the vibrator? (explanation of the stationary waves patterns on a vibrating string)
crest reverses its phase when it reflects at the fixed end + travels back along the string as a trough
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)
it reflects and reverses phase again, travelling away from the vibrator once more as a crest
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)
by a crest created by the vibrator
amplitude of wave increased
this is how stationary wave formed
What is the key condition for stationary waves to be formed? (explanation of the stationary waves patterns on a vibrating string)
time taken for wave to travel along string and back should be equal to time taken for whole number of cycles of vibrator
What is the equation for the time taken for a wave to travel along the string and back?
t = 2L/c
c- speed of waves on string
What is the equation for the time taken vibrator to pass through a whole number of cycles?
m/f
f- frequency
m- whole number
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)
2L/c = m/f
At what frequencies are stationary waves formed?
f, 2f, 3f, etc
What is the equation for the length of the vibrating section of the string?
L = mλ/2 = whole number of half wavelengths
What does the pitch of a note correspond to?
frequency
How can the pitch of a note from a stretched string be altered?
by changing the tension of the string or by altering its length
What does raising the tension do to the pitch?
increases pitch
What does shortening the length do to the pitch?
increase pitch
What does lowering the tension do the pitch?
lowers the pitch
What does increasing the length do to the pitch?
lowers the pitch
How can a vibrating string/ wire be tuned to the same pitch as a tuning fork?
by changing the length or altering the tension
What is the difference between a vibrating string and tuning fork? (hint- frequencies)
sound from a vibrating string includes all the harmonic frequencies, whereas a tuning fork vibrates only at a single frequency
When is a wire tuned?
when its first harmonic frequency is the same as the tuning fork frequency
Equation for the first harmonic frequency
f = 1 root T/ µ
—-
2L
T- tension
µ- mass per unit length
What is a simple visual check when using a tuning fork to tune a wire?
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
