Question
42. A sound wave in air has a period of .0015 s . What is the approximate wavelength of the sound wave? Remember that the average speed of sound in air is \( 343 \mathrm{~m} / \mathrm{s} \).
Ask by Young Henry. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The approximate wavelength of the sound wave is 0.51 meters.
Solution
1. The period of the sound wave is given as
\[
T = 0.0015\, \text{s}.
\]
2. The frequency \( f \) is the reciprocal of the period:
\[
f = \frac{1}{T} = \frac{1}{0.0015\, \text{s}} \approx 666.67\, \text{Hz}.
\]
3. The wavelength \( \lambda \) is found using the formula:
\[
\lambda = \frac{v}{f},
\]
where the speed of sound in air is
\[
v = 343\, \text{m/s}.
\]
4. Substituting the values:
\[
\lambda = \frac{343\, \text{m/s}}{666.67\, \text{Hz}} \approx 0.5145\, \text{m}.
\]
5. Therefore, the approximate wavelength of the sound wave is:
\[
\lambda \approx 0.51\, \text{m}.
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the wavelength of the sound wave, you can use the formula: \( \text{Wavelength} = \text{Speed} \times \text{Period} \). Given that the speed of sound in air is 343 m/s and the period is 0.0015 s, the wavelength would be \( 343 \, \text{m/s} \times 0.0015 \, \text{s} = 0.5145 \, \text{m} \) or approximately 0.51 meters. Now, the calculation assumes ideal conditions, but remember that various factors, like humidity and temperature, can affect sound speed. It's always good to keep those in mind especially in real-world applications such as sound engineering or acoustics!
