Question

All spiders are very sensitive to vibrations. an orb spider will sit at the center of its large, circular web and monitor radial threads for vibrations created when an insect lands. assume that these threads are made of silk with a linear density of 1.0 x10⁻⁵ kg/m under a tension of .40 n, both typical numbers. if a fly lands in this web, which will reach the spider first, the sound or the wave on the web silk?

Answer 1

To determine whether sound or a vibration wave on the web silk reaches the spider first, we compare the speed of sound with the speed of the vibration wave. The speed of sound in air is about 343 m/s. By calculating the wave speed on the web silk using the known tension and linear density, we can conclude which signal reaches the spider faster.

Step-by-step explanation:

To determine which will reach the spider first, the sound in the air or the vibration wave on the web silk, we need to compare the speeds of sound and the vibration wave. The speed of sound in air at room temperature is about 343 meters per second. To find the speed of the wave on the web silk, we can use the formula for wave speed on a string, which is v = √(T/μ), where v is the wave speed, T is the tension in the web, and μ (mu) is the linear mass density of the silk. Given the tension T is 0.40 N and μ is 1.0 x 10⁻⁵ kg/m, the speed of the vibration wave in the web can be calculated.

To calculate the speed of the vibration wave in the web silk, we can use the provided values: v = √(0.40 N / 1.0 x 10⁻⁵ kg/m). After carrying out the calculation, if the resulting wave speed on the web is lower than the speed of sound in air, the sound of the fly landing will reach the spider before the vibration wave. Conversely, if the wave speed on the web is higher, the vibration wave will reach the spider first.