Final answer:
To find the new wavelength of a sound wave when its frequency doubles, we use the constant speed of the original wave, then divide by the new frequency. The result is that the new wavelength is half of the original, leading to an answer of 1.0 meter when the frequency is changed from 170 Hz to 340 Hz.
Step-by-step explanation:
The question is asking to determine the new wavelength of a sound wave when its frequency is increased from 170 Hz to 340 Hz, given that the original wavelength is 2.0 meters. The relationship between the frequency (f), wavelength (λ), and speed (v) of a wave is given by the equation v = f λ. Assuming the speed of sound in air remains constant, the new wavelength can be calculated using the original wave's speed, which is the product of the original frequency and wavelength.
To find the new wavelength (λ'), use the equation v = f' λ', where f' is the new frequency. First, calculate the speed of sound using the original frequency and wavelength: v = 170 Hz × 2.0 m = 340 m/s. Then, solve for the new wavelength: λ' = v / f' = 340 m/s / 340 Hz = 1.0 m. Therefore, the new wavelength when the frequency is 340 Hz is 1.0 meter.