QUESTION IMAGE
Question
in which of the following locations can a person hear the echo of a sound? a) at least 33.2 meters behind the reflecting surface b) less than 16.6 meters in front of the reflecting surface
To hear an echo, the time between the original sound and its reflection must be at least 0.1 seconds (so the brain can distinguish them). The speed of sound in air is approximately 332 m/s. Using the formula \( d=\frac{v\times t}{2} \) (since the sound travels to the reflecting surface and back), for \( t = 0.1\space s \), \( d=\frac{332\times0.1}{2}= 16.6\space m \). But the distance from the source to the reflecting surface needs to be such that the total round - trip distance allows the time delay. Wait, actually, the minimum distance from the person to the reflecting surface to hear an echo is about 16.6 meters. But option A says "at least 33.2 meters behind the reflecting surface" – wait, no, let's re - calculate. Wait, the formula is \( \text{Distance}=\frac{\text{Speed of sound}\times\text{Time interval}}{2} \). The time interval for echo perception is about 0.1 s. So \( \text{Distance}=\frac{332\space m/s\times0.1\space s}{2}=16.6\space m \). But if we consider the distance behind the reflecting surface, the sound has to go to the surface and back. Wait, maybe there's a mis - statement in the options. Wait, the correct condition is that the distance from the person to the reflecting surface should be at least 16.6 meters so that the time taken for the sound to go and come back is at least 0.1 s (since \( t=\frac{2d}{v} \), so \( d=\frac{v\times t}{2} \)). But option A: "At least 33.2 meters behind the reflecting surface" – if we consider that the sound has to travel to the surface and back, so the distance from the person to the surface is \( d \), then the round - trip distance is \( 2d \). If \( d = 16.6\space m \), round - trip is 33.2 m. So if a person is at least 33.2 meters behind the reflecting surface, the sound has to travel 33.2 meters (to the surface and back? No, wait, "behind the reflecting surface" – maybe the wording is that the distance from the person to the reflecting surface is such that the sound travels to the surface and back to the person. So if the person is \( x \) meters behind the surface, the sound travels \( x \) meters to the surface and \( x \) meters back, total \( 2x \). We need \( 2x\geq v\times t \), with \( t = 0.1\space s \), \( v = 332\space m/s \), so \( 2x\geq332\times0.1 = 33.2\space m \), so \( x\geq16.6\space m \). Wait, no, the option A says "at least 33.2 meters behind the reflecting surface" – maybe the option has a wording issue, but let's analyze the options. Option B says "Less than 16.6 meters in front of the reflecting surface" – in that case, the round - trip distance is less than \( 2\times16.6 = 33.2\space m \), so the time taken is less than \( \frac{33.2}{332}=0.1\space s \), so the brain can't distinguish the echo. So to hear the echo, the distance should be such that the round - trip time is at least 0.1 s, so the distance from the person to the reflecting surface (or behind, depending on wording) should be such that \( 2d\geq33.2\space m \) (so \( d\geq16.6\space m \) from the surface). But option A says "at least 33.2 meters behind the reflecting surface" – maybe the "behind" is a mis - wording, and it's supposed to be the distance from the person to the surface such that the round - trip is 33.2 m. So option A is the correct one because for the echo to be heard, the sound must travel a round - trip distance of at least \( v\times t = 332\times0.1 = 33.2\space m \) (so the distance from the person to the reflecting surface and back is at least 33.2 m, meaning the person is at least 16.6 m from the surface, but option A's wording might be considering the total round -…
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
A) At least 33.2 meters behind the reflecting surface