What determines rent prices of houses? Does it depend only on interest rates?
What you're referring to is called the "rental yield", i.e. income generated from rentals as a portion of the amount you have invested in the house.

The interest rate is definitely one of the factors determining rental prices. Most other factors would be included in the house price (e.g. how big and nice the house is, how many bedrooms, are there many workplaces around, crime rate, etc.)

Other things that might be left out apart from the interest rate and house price is how competitive the house rental market is. You could imagine a neighborhood where there's only a few houses that are for rent. If there's demand, there's no reason the rental yield should be lower than another neighborhood with more competitive rental market.

If a person buys a house as an investment, then he/she would have taken into account the return he/she would get if this money was invested elsewhere. Say the average stock market return is about 7%, then it makes no sense for a person buying a house as an investment to seek for rental yield lower than that.

Having said that, of course, you need to take into account property price increase as well. You might be ok getting lower rental yield than your next best option if you foresee that the house price in your neighborhood would rise in the future.

Lastly, if you have a house and need to move away for a few years knowing that you'll eventually move back, it might be a good choice to rent it out in the meantime. For this, your primary reason of owning that house is not for investment, so you might be ok with getting lower rental yield (perhaps in exchange for being able to select suitable renters).