High School

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A harmonic wave is traveling along a rope. It is observed that the oscillator generating the wave completes 37.6 vibrations in 27.9 seconds. Also, a given maximum travels 450 cm along the rope in 11.3 seconds.

What is the wavelength?

Answer in units of cm.

Answer :

Answer:

[tex]\lambda = 25.79\ cm[/tex]

Explanation:

given,

Wave vibrates = 37.6

time = 27.9 s

maximum distance travel = 450 cm

time = 11.3 s

wavelength = ?

frequency of wave

[tex]f=\dfrac{37.6}{27.9}[/tex]

f = 1.35 Hz

Speed of wave

[tex]v = \dfrac{450}{11.3}[/tex]

v = 39.82 cm/s

wavelength of wave

v = fλ

[tex]\lambda =\dfrac{v}{f}[/tex]

[tex]\lambda =\dfrac{34.82}{1.35}[/tex]

[tex]\lambda = 25.79\ cm[/tex]

Hence, wavelength of the wave is equal to 25.79 cm.

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Rewritten by : Barada

Final answer:

The wavelength of a wave can be calculated using the speed of the wave and its frequency. In this case, the wavelength is 29.50 cm.

Explanation:

Wavelength: The wavelength of a wave is the distance between two similar points on the medium that have the same height and slope. In this case, the wavelength can be found using the formula: λ = v/f, where v is the speed of the wave and f is the frequency.

Given Data: Number of vibrations = 37.6, Time = 27.9 s, Distance traveled = 450 cm, Time = 11.3 s.

Calculation: Speed of the wave = Distance/Time = 450 cm / 11.3 s = 39.82 cm/s. Frequency = Number of vibrations / Time = 37.6 / 27.9 = 1.35 Hz. Therefore, Wavelength = 39.82 cm / 1.35 Hz = 29.50 cm.