Worksheet: Beats

In this worksheet, we will practice comparing superimposed waves of similar frequencies to calculate the beat frequency resulting from their superposition.

Q1:

The middle C hammer of a piano hits two strings, producing beats of frequency 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?

  • A 260.50 Hz and 259.50 Hz
  • B 261.00 Hz and 258.00 Hz
  • C 260.50 Hz and 258.50 Hz
  • D 261.50 Hz and 258.50 Hz
  • E 261.50 Hz and 259.50 Hz

Q2:

A piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz.

What beat frequency is produced by the 128.3 Hz and 128.1 Hz notes?

What beat frequency is produced by the 127.8 Hz and 128.3 Hz notes?

What beat frequency is produced by the 128.1 Hz and 127.8 Hz notes?

Q3:

Two identical strings, of identical lengths of 2.00 m and linear mass density πœ‡ = 0 . 0 0 6 5 0 / k g m , are fixed on both ends. String 𝐴 is under a tension of 120.00 N. String 𝐡 is under a tension of 130.00 N. They are each plucked and produce sound at the 𝑛 = 1 0 mode. What is the beat frequency?

Q4:

A string of linear mass density πœ‡ = 0 . 0 0 6 0 0 0 0 / k g m and length 𝐿 = 1 . 5 0 0 0 m , is fixed at both ends and is under a tension of 155.00 N. It oscillates in the 𝑛 = 1 0 mode and produces sound. A tuning fork is ringing nearby, producing a beat frequency of 23.76 Hz.

What is the frequency of the sound from the string?

What is the frequency of the tuning fork if the tuning fork frequency is lower?

What should be the tension of the string for the beat frequency to be zero?

Q5:

A car has two horns, one emits a frequency of 138 Hz and the other emits a frequency of 296 Hz. What beat frequency do they produce?

Q6:

On a piano, the F, F-sharp, and A keys (within the same octave) are struck simultaneously, producing frequencies of 352 Hz, 370 Hz, and 440 Hz. What is one beat frequency produced by this discordant combination that is greater than 70 Hz?

Q7:

A string with a linear mass density of 0.00620000 kg/m is stretched between two posts 1.30000 m apart. The tension in the string is 150.000 N. The string oscillates and produces a sound wave. A 1 0 2 4 . 0 0 Hz tuning fork is struck and the beat frequency between the two sources is 52.83 Hz.

What is the frequency of the wave on the string?

What is the wavelength of the wave on the string?

Q8:

Twin jet engines on an aeroplane are producing an average sound frequency of 4 1 0 0 . 0 0 0 Hz. The engines produce a beat frequency of 0.500 Hz. What are the engines’ individual frequencies?

  • A 4 0 9 9 . 5 7 0 Hz and 4 1 0 0 . 5 2 0 Hz
  • B 4 0 9 9 . 5 7 0 Hz and 4 1 0 0 . 7 5 0 Hz
  • C 4 0 9 9 . 7 5 0 Hz and 4 1 0 0 . 5 5 0 Hz
  • D 4 0 9 9 . 7 5 0 Hz and 4 1 0 0 . 2 5 0 Hz
  • E 4 0 9 9 . 5 7 0 Hz and 4 1 0 0 . 2 5 0 Hz

Q9:

Two tuning forks having frequencies of 330 Hz and 354 Hz are struck simultaneously.

What average frequency do they produce?

What beat frequency do they produce?

Q10:

What beat frequency results if the musical notes 𝐴 and 𝐢 are played together? The notes 𝐴 and 𝐢 have frequencies of 440 Hz and 261 Hz respectively.

Q11:

What beat frequency results if the musical notes 𝐷 and 𝐹 are played together? The notes 𝐷 and 𝐹 have frequencies of 293 Hz and 349 Hz respectively.

Q12:

A piano tuner hears a beat every 1.00 s when listening to a 164-Hertz-frequency tuning fork and a single piano string. What is the frequency of the string if it is of a lower frequency than the tuning fork?

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