4.6 More about stationary waves on strings

Question 1

Describe the first harmonic pattern of vibration?

Answer 1

» Antionode at the middle as well as a node on each end

Question 2

How can you calculate the first harmonic frequency?

Answer 2

» The distance between adjacent nodes is 1/2 the wavelength
» Therefore the wavelength = 2L
» Frequency = Speed/Distance
» Therefore first harmonic frequency = C/2L

Question 3

Describe the 2nd harmonic vibration?

Answer 3

» A node in the middle, so the string is in 2 loops

Question 4

How can you calculate the 2nd harmonic frequency?

Answer 4

» Wavelength of the waves = L
» As each loop has a length of half of a wavelength
» Therefore 2nd harmonic frequency = C/L = 2 x First harmonic frequency

Question 5

Describe the 3rd harmonic pattern of vibration?

Answer 5

» Where there are 4 nodes in total
» There are nodes at a distance of 1/3L from either end and an antinode at the middle
» 3/2L = One wavelength, so Wavelength = 2/3L
» Therefore frequency of the third harmonic vibration = 3c/2L = 3 x first harmonic frequency

Question 6

How is a stationary wave made on a vibrating string?

Answer 6

» The crest revers its phase when it reflects at the fixed end and travels back as a torough
» When it reachers the vibrator, it relfects and revers phase again
» This reinforces the crest made by the vibrator leading to superpositiong

Question 7

What is the time taken for a wave to travel along a string in a vibrator?

Answer 7

» Speed = Distance/Time
» Time = Distance/Speed
» Distance = 2L as it is the total wavelength
» 2L/C = Time

Question 8

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

Answer 8

» m/f
» f is the frequency
» m is a whole number

Question 9

What is the length of a vibration section of the string?

Answer 9

» 2L/c = m/f
» F = mc/2L, Wavelength = 2L/M
» L = mc/2f/ L = mxlambda/L

Question 10

How can the pitch of a note be increased or decreased?

Answer 10

» Corresponds to its frequency, can be changed by altering the tension of the string or by altering the length

Question 11

How can you increase the pitch?

Answer 11

» Rasing the tension or shortening the length

Question 12

How can you increase the pitch?

Answer 12

» Rasing the tension or shortening the length

Question 13

How can you decrease the pitch?

Answer 13

» Lowering the tension or increasing the length lowers the pitch

Question 14

What is the equation which shows the first harmonic frequency links with tension?

Answer 14

» F = 1/2L (Squareroot(T/u))
» Where T is the tension in the wire
» and its mass per unit length is u

Question 15

What is the number of loops equal to?

Answer 15

» Number of nodes -1

Question 16

What is frequency directly proportional to?

Answer 16

» K/l
» Where K is a constant, and l is the length

Question 17

What is the frequency also proportional to?

Answer 17

» Ksquareroot(T)
» Where k is a constant and T is tension

Question 18

How is a stationary wave created?

Answer 18

» Create progressive waves at one end of the string
» These waves reflect back to the other end, with approximately the same speed and the same amplitude/frequency
» The 2 waves interfere and superpose and certain points
» When 2 waves interfere destructively, nodes are formed
» When 2 waves interfere constructively, antiinodes are formed