Questions: Wavelength - The frequency separating audible waves and ultrasonic waves is considered to be 20 kHz. What wavelength is associated with this frequency? (Assume the speed of sound to be 340 m / s.) A) 1.7 cm B) 5.2 cm C) 34 cm D) 55 cm

Wavelength
- The frequency separating audible waves and ultrasonic waves is considered to be 20 kHz. What wavelength is associated with this frequency? (Assume the speed of sound to be 340 m / s.)
A) 1.7 cm
B) 5.2 cm
C) 34 cm
D) 55 cm
Transcript text: Wavelength - The frequency separating audible waves and ultrasonic waves is considered to be 20 kHz . What wavelength is associated with this frequency? (Assume the speed of sound to be $340 \mathrm{~m} / \mathrm{s}$.) A) 1.7 cm B) 5.2 cm C) 34 cm D) 55 cm
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Solution

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Solution Steps

Step 1: Convert kHz to Hz

The given frequency is 20 kHz. Since 1 kHz = 1000 Hz, we multiply 20 by 1000 to get 20,000 Hz.

Step 2: Calculate the wavelength

The speed of sound is given as 340 m/s. The formula relating speed (v), frequency (f), and wavelength (λ) is v = fλ. We want to solve for wavelength (λ), so we rearrange the formula to λ = v/f. Plugging in the values, we get λ = (340 m/s) / (20,000 Hz) = 0.017 m.

Step 3: Convert meters to centimeters

Since the answer choices are in centimeters, we need to convert the wavelength from meters to centimeters. Since 1 m = 100 cm, we multiply 0.017 m by 100 to get 1.7 cm.

Final Answer: The final answer is $\boxed{A}$

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