RP01: Stationary waves on a string

Question 1

What is a stationary wave?

Answer 1

A wave that stores, but does not transfer energy

Question 2

How do stationary waves from on a piece of string?

Answer 2

Two waves with same wavelength, travelling in opposite directions, interfere with each other. When this occurs, they undergo superposition and a stationary wave is formed.

Question 3

What is a node?

Answer 3

A node is a point of zero displacement in a standing wave.
They occur when two waves in antiphase and destructively interfere such that they completely cancel.

Question 4

What is an antinode?

Answer 4

A point of max displacement in a standing wave.
Occur when two waves that are in phase constructively interfere.

Question 5

Describe the arrangement of nodes and antinodes when the string is at fundamental frequency

Answer 5

One central antinode and a single node at each end.

Question 6

What apparatus is used to generate a wave in a piece of string?

Answer 6

A vibration generator, driven by a signal generator

Question 7

What apparatus used to alter length of string that is oscillating?

Answer 7

A bridge can be moved along to alter the length of the oscillating region

Question 8

Why should the signal generator be operated for several minutes before use?

Answer 8

Signal generator needs time for the frequency to stabilise

Question 9

What safety measures must you take?

Answer 9

A counterweight or g clamp should be used to produce counteracting moment that prevents stand from toppling over.
Never stand directly under a mass hanger, good practice to put padded bucket below hanger.

Question 10

How does the length of the string affect the frequency of the first harmonic?

Answer 10

Inverse relationship between string length and frequency of first harmonic. As string length increases, frequency decreases.

Question 11

How does the string’s mass per unit length affect the frequency of the first harmonic?

Answer 11

As mass per unit length increases the frequency of the first harmonic decreases

Question 12

How does the tension in the string affect the frequency of the first harmonic?

Answer 12

As the tension in the string increases the frequency of the first harmonic increases

Question 13

What equation is used to calculate the frequency of a string’s first harmonic?

Answer 13

f= (1/2l) sqrt(T/μ)

Question 14

How can the tension in a string be varied?

Answer 14

Attaching a mass hanger at the end of the string. As masses added, tension will increase.

Question 15

How can you measure the mass per unit length of a piece of string?

Answer 15

Measure the mass of a piece of string using a mass balance and then divide this by the length of the string.

Question 16

What is the advantage of using a long piece of string when measuring the mass per unit length?

Answer 16

The longer the piece of the string, the power the percentage uncertainty in the measurement

Question 17

Assuming all other factors remain constant, what is the effect of changing the frequency to double that of the first harmonic?

Answer 17

Result in the string resonating in its second harmonic

Question 18

What equation is used to determine speed of wave?

Answer 18

v=fλ

Question 19

When vibrating at fundamental frequency, what is the wavelength relative to the length of the oscillating string?

Answer 19

λ=2L

Question 20

How can wave speed be calculated from the string’s tension and mass per unit length?

Answer 20

v= sqrt(T/μ)

Question 21

When plotting a graph of T against L for a fundamental frequency, how can wave speed be determined?

Answer 21

Gradient will be L/T
Wave speed given by 2L/T so is 2 x gradient