Test: Waves And Sound

Explanation
The period of a pendulum is the time it takes for one complete swing. In this case, the pendulum completes 75 swings in 25 seconds. To find the period, we divide the total time by the number of swings. Therefore, the period of the pendulum is 0.33 seconds.

Explanation
During complete destructive interference, the interference of two waves results in the cancellation of their amplitudes. This occurs when the crest of one wave coincides with the trough of the other wave. In this case, a node is produced, which is a point of zero displacement or amplitude. A node represents a point of minimum or zero intensity in the wave pattern. Therefore, the correct answer is "node."

Explanation
Resonance is the property that allows the sound box of an acoustic guitar to increase the loudness of the sounds produced by the strings. When the strings vibrate, they create sound waves that resonate within the sound box, causing it to vibrate as well. This vibration amplifies the sound and produces a louder tone. Therefore, resonance is the correct answer as it explains how the sound box enhances the loudness of the guitar's sound.

Explanation
The first antinode is created at a distance of one-fourth of the wavelength from the wall. Since the wavelength is 15 cm, one-fourth of that is 3.75 cm. Therefore, the first antinode is created 3.75 cm from the wall.

Explanation
When two trumpets are played together, beats are heard due to the interference between the two sound waves. The number of beats heard is equal to the difference in frequency between the two trumpets. In this case, 20 beats are heard in 4.0 seconds. Since the frequency of the lower pitched trumpet is given as 440 Hz, we can calculate the frequency of the higher pitched trumpet by adding the number of beats to the frequency of the lower pitched trumpet. Therefore, the frequency of the higher pitched trumpet is 440 Hz + 20 beats/4.0 s = 445 Hz.

Explanation
When the tension in a vibrating string is quadrupled, the frequency of the string also quadruples. Since the initial frequency is 800 Hz, quadrupling it will result in a frequency of 1600 Hz.

Explanation
In the context of standing waves on a string, nodes are points where the amplitude of the wave is always zero. The third overtone refers to the third harmonic, which has three complete waves within the length of the string. For a string fastened at both ends, the number of nodes in a standing wave is equal to one more than the number of complete waves. Since the third overtone has three complete waves, there should be four nodes. Thus, the given answer of "five" is incorrect.

Explanation
The length of the air column is 1 m because the third resonant length of a closed air column is equal to three-fourths of the wavelength. Since the wavelength is given as 80 cm, three-fourths of 80 cm is 60 cm, which is equal to 1 m. Therefore, the length of the air column is 1 m.

Explanation
When a guitar string is plucked, it vibrates back and forth perpendicular to the direction of the wave propagation. This type of motion is characteristic of transverse waves, where the particles of the medium move perpendicular to the direction of energy transfer. Therefore, the waves produced on a guitar string by plucking it are transverse waves.

Explanation
The frequency of a note that is four octaves lower than 880 Hz is 55 Hz. Each octave represents a doubling of the frequency, so going four octaves lower means dividing the frequency by 2 four times. 880 Hz divided by 2 four times gives us 55 Hz.

Explanation
When standing waves are formed on a string fastened at both ends, the nodes are the points on the string that do not move. The number of nodes in an overtone is equal to the number of segments or loops formed on the string. In the third overtone, there are 2 complete loops and 1 half loop, resulting in a total of 5 nodes. Therefore, the correct answer is 5.

Explanation
The first and second resonant lengths of an air column that is closed at one end can be expressed as λ/4 and 3λ/4, respectively, where λ is the wavelength of the wave. By solving these equations, we find that λ = 60 cm. Therefore, the best value for the wavelength of the wave is 60 cm.