11.3.2 Standing Waves on a String

Question 1

Standing Waves on a String

Answer 1

• A string that is fixed at both ends can only support standing waves of certain wavelengths and frequencies.
• The wavelength of the nth normal mode of a string must satisfy the equation .
• The normal mode with the longest allowable wavelength is called the first harmonic, or the fundamental. The second harmonic has half the wavelength and twice the frequency, and the third harmonic has one-third the wavelength and three times the frequency.

Question 2

The F string on a guitar is out of tune. How do you adjust the frequency of the string to tune the guitar?

Answer 2

Adjust the tension

Question 3

The fundamental frequency of a guitar string is 220 Hz. Which of the following is the frequency of the fourth harmonic?

Answer 3

880 Hz

Question 4

Which of the following expressions gives the fundamental frequencies of a standing wave on a string of length L?

Answer 4

• f = nu/2L
• f = n(wavelength)/2LT
• f = nf1

Question 5

The figure shows a standing wave on a rope of length of L. Which of the following is the wavelength of the wave?

Answer 5

wavelength = 2/5L

Question 6

Suppose a standing wave is generated on a string of length L. If the string is fixed at each end, which of the following is the relationship between the nodes and antinodes?

Answer 6

There is always one more node than antinodes.

Question 7

How many nodes and antinodes are there in the standing wave shown in the figure?

Answer 7

five nodes; four antinodes

Question 8

The fundamental wavelength of a string that is fixed at both ends, also known as first harmonic, is smaller than all the other harmonics

Answer 8

false

Question 9

What is the required length for a string to have its third harmonic vibrate at 300 Hz at 600 m / s?

Answer 9

3 m