A solenoid inductor (self-inductance of 96 mH) is 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center (approximately same diameter). The coil's resistance is 6.0 ohms. The mutual inductance between the coil and solenoid is 31 μH. At a given instant, the current in the solenoid is 540 mA and is decreasing at the rate of 2.5 A/s. At this given instant, what is the magnitude of the induced current in the coil?

Wo audio speakers are placed on a vertical rail. speaker a is placed at head-level while speaker b is place at some variable height, \delta yδy, above speaker a. both speakers receive simultaneous input from a sine-wave generator so the speakers each produce a pure sinusoidal sound wave with a wavelength of 0.531 meters. calculate the lowest height that speaker b can be placed above speaker a to produce a minimum of sound heard by person standing \delta x = 7.86δx=7.86 meters directly in front of speaker a.

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz. what wavelength is produced?