What are the longest and shortest wavelengths of sound that can be heard by a bat in air where the speed of sound is $343\text{ m/s}$?

• A. $0.686\mathrm{mm}\text{to}0.343\mathrm{m}$
• B. $3.00\mathrm{mm}\text{to}0.150\mathrm{m}$
• C. $17.2\mathrm{mm}\text{to}17.2\mathrm{m}$
• D. $5.83\mathrm{m}\text{to}292\mathrm{m}$
• E. $3.43\mathrm{mm}\text{to}172\mathrm{mm}$

Answer: (E)

Verified step by step guidance

1. Understand that the problem is asking for the range of wavelengths of sound that a bat can hear, given the speed of sound in air is 343 m/s.
2. Recall the relationship between speed, frequency, and wavelength of a wave: \( v = f \lambda \), where \( v \) is the speed of sound, \( f \) is the frequency, and \( \lambda \) is the wavelength.
3. To find the longest wavelength, use the lowest frequency a bat can hear. Rearrange the formula to \( \lambda = \frac{v}{f} \) and substitute the lowest frequency value.
4. To find the shortest wavelength, use the highest frequency a bat can hear. Again, use the formula \( \lambda = \frac{v}{f} \) and substitute the highest frequency value.
5. Compare the calculated wavelengths with the given options to determine which range matches the calculated values.