Beats Practice Problems

A set of hollow pipes are closed on one end by immersing them in water, leaving only one open end. The lengths of the pipe above the water differ by 20.0 cm. Determine the beat frequency for a pipe with a length of 2.0 m above the water and i) a longer pipe ii) a shorter pipe. (Consider waves with fundamental frequency only)

A childhood game involves tying light gauge polythene papers together and attaching a small mass on one end of the polythene paper string. The mass is swung in a circle using the polythene paper string emitting sound. Suppose a child is rotating a mass at 163 rpm when an observer hears a 0.50 Hz frequency due to the presence of another child rotating a second mass. i) determine two possible rotational frequencies in RPM for the second mass. ii) When the rotational speed of the second mass is decreased, the beat frequency decreases to 0.40 Hz. Which of the values determined in i) is the true rotational frequency of the second mass? 

Two violinists are tuning their equipment to simultaneously play a note of wavelength 773 mm. However, one piece of equipment produces a note of wavelength 767 mm, which is different from the desired wavelength. Determine the beat frequency an observer will detect from the two pieces of equipment played together. 

Musicians often tune their instruments before a performance to ensure accurate pitch. Suppose a guitarist tunes his instrument by adjusting two strings to oscillate precisely at 250 Hz. Later, he notices that one of the strings is slightly out of tune and increases its tension. This change results in four beats per second being audible when the two strings vibrate simultaneously. Determine the new frequency of the string with the increased tension.

A saxophonist detects six beats per second when playing a note on their saxophone and comparing it with a 784 Hz chime. Through adjustments in the position of the mouthpiece (pulling it out), the saxophonist is able to align the frequency with the chime. Determine the initial frequency of the saxophonist's played note.

An orchestral harpist is fine-tuning his harp to ensure that the notes are accurately tuned. When in tune, note C should be at a frequency of 523 Hz, and note G should be at 784 Hz. Compared with a properly tuned C string, the harpist finds the G string's tension to be somewhat low, so he tightens the string in small increments until it reaches the desired level. Determine the frequency of the G string when the harpist detects a difference of five beats per second.

Suppose you have a pair of identical tuning forks, producing sound waves at a frequency of 523 Hz. Holding one of the tuning forks steady, you let the other fall from a 15-meter-high ledge. Ignoring air resistance determine the total beats you will hear before the plummeting tuning fork impacts the surface.

What is the vibrational frequency of a banjo string that produces 4 beats per second when played alongside a 440-Hz tuning fork and 9 beats per second when played alongside a 445-Hz tuning fork? Describe your reasoning.

A musician plays a note on his organ pipe open at both ends and produces a note that resonates with a glass tube partially filled with liquid mercury when its length from top to surface of mercury is measured as 0.15 m and then again at 0.45 m. What would be the frequency of this note? Assume the speed of sound in air is 343 m/s.

Two people are facing each other holding identical tuning forks in their hands. The tuning forks are struck simultaneously producing sound at a frequency of 250 Hz but due to a slight defect in one fork, it produces sound that is initially 180° out-of-phase compared to the other. What should be the minimum separation between these two forks for complete constructive interference to occur at some point between the two people? Assume air temperature as T = 25°.

What will be the beat frequency heard when two guitar strings, initially tuned to the same frequency of 298 Hz, are played together after the tension in one string is decreased by 3.0%? [Hint: $f^{\prime}=\frac{1}{\lambda}\sqrt{\frac{F_{T}^{\prime}}{\frac{m}{L}}}$ ]

What is the number of beats per second that will be heard when an experimental prototype drone emits sound waves with wavelengths of 2.6 m and 2.8 m in the air at a temperature of 22°C?

What is the minimum distance between the regions of maximum sound intensity in space for sounds emitted by a newly designed sound system that produces sound waves with wavelengths of 2.74 m and 2.92 m in the air? Assume that the speed of sound in air is 343 m/s.

A cellist hears one beat every 4.0 s while adjusting two strings, with one producing a sound at a frequency of 350 Hz. How much does the other string's frequency differ from this?